We are interested in studying the following sum, which is the von Mangoldt convolution analogue to the problem in Section 2 of
[1]}:
\(\mathcal {N}^U_{0,\Lambda _k}(A;h)=\sum _{\begin{array}{c}f\in I(A;h)\\f(0)\ne  0\end{array}}\Lambda _k(f).\) 
